3578edo

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← 3577edo

3578edo

3579edo →

Prime factorization	2 × 1789
Step size	0.335383 ¢
Fifth	2093\3578 (701.956 ¢)
Semitones (A1:m2)	339:269 (113.7 ¢ : 90.22 ¢)
Consistency limit	21
Distinct consistency limit	21

3578edo is consistent in the 21-odd-limit. It inherits the 2.5.11.13.29.31 subgroup mapping from 1789edo and tempers out the jacobin comma. Although it significantly improves the 2.3.17.19 subgroup, it does have a pretty rough 7th harmonic, with the roughly the same relative error as in 1789edo and is best considered as a 2.3.5.11.13.17.29.29.31 subgroup tuning.

Prime harmonics

Approximation of prime harmonics in 3578edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.001	+0.047	+0.095	+0.052	-0.058	+0.019	-0.028	-0.102	+0.048	-0.038
	Relative (%)	+0.0	+0.4	+14.1	+28.4	+15.4	-17.3	+5.8	-8.5	-30.5	+14.4	-11.4
Steps (reduced)		3578 (0)	5671 (2093)	8308 (1152)	10045 (2889)	12378 (1644)	13240 (2506)	14625 (313)	15199 (887)	16185 (1873)	17382 (3070)	17726 (3414)